Springer Science & Business Media, Mar 2, 2009 - Science - 461 pages
"An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the near-impossible—it has made a subject which is generally inhospitable to nonspecialists because of its ‘family jargon’ appear nonintimidating even to a beginning graduate student."
—The Journal of the Indian Institute of Science
"The book under review gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/set-valued analysis. It includes...results with many historical comments giving the reader a sound perspective to look at the subject...The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis."
"I recommend this book as one to dig into with considerable pleasure when one already knows the subject...‘Set-Valued Analysis’ goes a long way toward providing a much needed basic resource on the subject."
—Bulletin of the American Mathematical Society
"This book provides a thorough introduction to multivalued or set-valued analysis...Examples in many branches of mathematics, given in the introduction, prevail [upon] the reader the indispensability [of dealing] with sequences of sets and set-valued maps...The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work...Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to set-valued analysis."
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125 4.1.3 Adjacent and Clarke Tangent Cones 126 4.1.4 Sleek Subsets 130 4.1.5 Limits of Contingent Cones; ... Image 153 4.4 Normal Cones 156 4.5 Other Tangent Cones 159 4.5.1 Convex Kernel of a Cone 159 4.5.2 Paratingent Cones 160 4.5.3 ...
4.5.3 Hypertangent Cones 164 4.5.4 A Menagerie of Tangent Cones 165 4.6 Tangent Cones to Sequences of Sets 166 4.7 Higher Order Tangent Sets 171 5 Derivatives of Set- Valued Maps 179 5.1 Contingent Derivatives 181 5.2 Adjacent and ...
104 4.1 Contingent Cone at a Boundary Point may be the Whole Space 122 4.2 The Graph of T[aM (•) 123 4.3 Counterexample: Tangent Cone to the Intersection . . 142 4.4 The Menagerie of Tangent Cones: they may be all different 161 5.1 ...
We obtain in this way a variety of closed cones made of what we call tangent vectors. The most popular of these tangent cones is for the time the contingent cone introduced in the thirties by Bouligand, (which is the upper limit of ...
Therefore, in the framework of a given problem, we can regard a tangent cone to the graph of the set-valued map F at ... Derivatives built in this way from the various choices of tangent cones are called graphical derivatives and the ...